# NUMBER SYSTEM

1. Find the sum of the first 41 odd numbers.
A) 1536     B) 1681     C) 1875     D) 1456

2. Find the sum of the first 91 even numbers.
A) 8725    B) 8945    C) 8272    D) 8372

3. Find the unit digit in the product of
421 × 1654 × 186 × 236
A) 4     B) 1     C) 2     D) 6

4. If 22x-5 = 16, then the value of x is ....
A) 4     B) 4.5     C) 5     D) 5.5

8. A number when divided by 533 gives a remainder 49. If the same number is divided by 41, the remainder will be .....
A) 3     B) 1        C) 8        D) 4

9. A number when divided by 585 gives a remainder 41. If the same number is divided by 39, the remainder will be .....
A) 8        B) 5        C) 1         D) 2

14. The sum of first 60 natural numbers is:
A) 1450         B) 1960       C) 1830         D) 1870

15. What least value must be given to ‘b’ so that the number 91873b6 is divisible by 9?
A) 4       B) 7       C) 2        D) 9

16. The sum of two numbers is 16 and their product is 60. What will be the sum of their reciprocals?

17. In an examination, 20% of the candidates failed in Mathematics and 30% in English. If 15% failed in both Mathematics and
English, then what is the percentage of students who passed in both the subjects?
A) 45%           B) 55%          C) 65%             D) 60%

18. What is the unit digit of 1! + 2! + 3! + ....... + 99! + 100!?
A) 3              B) 5               C) 2                D) 1

19. If one-fifth of one-third of a number is 39, then four-fifth of the number is .....
A) 210             B) 245              C) 468                D) 490

20. If the sum and the product of two numbers are 11 and 24 respectively then the difference of the numbers must be .....
A) 3             B) 6                C) 5           D) 1

21. The sum of the five consecutive numbers is equal to 80. What is the product of largest and the smallest numbers?
A) 320            B) 350             C) 420                   D) 450

22. What is the least value assigned to # so that the number 45458#8 is divisible by 8?
A) 1       B) 6             C) 4                  D) 2

23. The ratio between two numbers is 7 : 8 and their sum is 900. What is the greater of the two numbers?
A) 490             B) 480                C) 460              D) 450

24. One - sixth of three - eighth of a number is 36. Find that number.
A) 574      B) 576             C) 840               D) 842

25. The ratio between two numbers is 6 : 7 and their sum is 910. What is the greater of the two numbers?
A) 409              B) 420               C) 421             D) 473

Key:  1-B; 2-D; 3-A; 4-B;  5-C; 6-D; 7-C; 8-C; 9-D; 10-D; 11-C; 12-C; 13-C; 14-C; 15-C; 16-C; 17-C; 18-A; 19-C; 20-C; 21-A; 22-C; 23-B; 24-B; 25-B

Explanations

1. We know that,
Sum of first n odd numbers = n2
Given, n = 41
Required sum = (412) = 41 × 41 = 1681

2. We know that,
Sum of first n even numbers = n(n + 1)
Given, n = 91
Required sum = 91(91 + 1) = 91 × 92 = 8372

3. Product of unit digits = 1 × 4 × 6 × 6 = 144
Required unit digit = 4

4. 22x - 5 = 16,
22x - 5 = 24
If bases are equal, then powers also should be equal.
2x − 5 = 4 ⇒ 2x = 9 ⇒ x = 4.5

Some More...

A golden opportunity for Bank exams aspirants. Thousands of posts in SBI and other Banks. Out of five papers in the SBI clerk exam, Quantitative Aptitude plays major role. Arithmetic and Data Interpretation questions will be there in this paper. Arithmetic is the maths, which we use in our day-to-day life. As arithmetic chapters are there upto 10th class only all the aspirants inclusive of non-maths might have studied this. By understanding all the chapters thoroughly and with a lot of practice it is not difficult to solve all the questions of the paper. Also important is simplifications. Out of 40 questions in Q.A., 20 are simplification questions. Students need to mug up tables upto 20, squares of numbers upto 25 and cubes of numbers upto 15 to make simplifications easy. They also learn Speed Maths for solving simplification questions in seconds without pen. All the chapters in arithmetic have to be practiced thoroughly. Let us see all the chapters of arithmetic in detail.

Digit: 0 to 9 are the digits.

Number: By using digits we write numbers.

Face Value: The real value of the digit.

Place Value: The value of the digit according to the place.

e.g.: In 2794, the face value of 7 is '7'and the place value is '700

Classification of Numbers:

Odd Numbers

Numbers which are not divisible by 2

e.g.: 1, 3, 5, 7, .......

Even Numbers

Numbers which are divisible by 2

e.g.: 2, 4, 6, 8, .......

Natural Numbers
All counting numbers             e.g.: N = {1, 2, 3, ........}
Sum of first 'n' natural numbers is
Sum of squares of first 'n' natural numbers is
Sum of cubes of first 'n' natural numbers is

Whole Numbers
0 and all natural numbers
e.g.: W = { 0, 1, 2, 3, ...}

Integers
Natural numbers, zero and negative of natural numbers
e.g.: I = { ........, -3, -2, -1, 0, +1, +2, +3, .......}
Rational Numbers
These are of the form of p/q, where q π 0
e.g.:  etc

Irrational Numbers
Can't be written in p/q form, where q ≠ 0
e.g.:  π  etc

Composite Numbers
Numbers having more than two factors

Prime Numbers
Numbers divisible by one and the number itself or numbers having only two factors.
e.g.: 2, 3, 5, 7, 11, 13, ...... etc
* All prime numbers end with 1, 3, 7 or 9 except 2 and 5.
*  is the only even prime number.
*   '1' is neither a prime nor composite number. It is a unitary.
*  There are 25 prime numbers upto 100.

Twin prime numbers
The difference between two prime numbers is '2'.
e.g.: 3 - 5, 5 - 7, 11 - 13 etc

Co prime numbers
Numbers not having any common factors.
e.g.: 3, 5 and 8 are co primes to each other.

Some important Identities:
* (a + b)2 = a2 + b2 + 2ab
* (a − b)2 = a2 + b2 − 2ab

* (a + b) (a − b) = a2 − b2
*(a + b)3 = a3 + b3 + 3a2 b + 3ab2
* (a − b)3 = a3 − b3 − 3a2 b + 3ab2
* a3 + b3 = (a + b) (a2 − ab + b2)
* a3 − b3 = (a − b) (a2 + ab + b2)
* (a + b + c)2 = a2 + b+ c2 + 2ab + 2bc + 2ac
* a3 + b3 + c3 − 3abc = (a + b + c) (a2 + b2 + c2 − ab − bc − ac)

e.g.:
1) 2.01            2) 2             3) 1                 4) 1.93                5) None of these
Sol: It is based on the formula a3 + b3 = (a+b)(a2−ab+b2)
∴ 1.07 + 0.93 = 2, hence answer (2).

To solve the equations based on numbers, the number is written in algebraic form.
For example let the number be x.

The numerator of a fraction is written in the following form
Three-fourth of a number =
Two-third of a number =
Double of a number = 2x, Thrice of a number = 3x
20% of a number =
30% of 3/4 of one-third of a number =

e.g.: 1.  4/5  of  4/7  of  5/6  of  1218 = ?     (SBI 2008)
(A) 415          (B) 384        (C) 492           (D) 346          (E) None of these
sol:

2. One-seventh of a number is 51. What will be 64% of that number?       (SBI 2008)
(A) 248.12          (B) 228.48           (C) 238.24          (D) 198.36             (E) None of these
Sol:

3. If (16)3 is subtracted from the square of a number, the answer so obtained is 3825. What is the number ?      (SBI 2008)
(A) 69          (B) 59              (C) 89              (D) 79            (E) None of these
Sol: Let the number be x
x2 − 163= 3825 --- x = 89

4. If (92)2 is added to the square of a number, the answer so obtained is 10768. What is the number?          (SBI 2008)
(A) 46           (B) 2304        (C) 48             (D) 2116              (E) None of these
Sol: Let the number be x
x2 + 922= 3825    x = 48

5. If an amount of Rs. 97,836 is distributed equally amongst 31 children. How much amount would each child get?    (SBI 2008)
(A) Rs.3,756        (B) Rs.3,556       (C) Rs. 3,356       (D) Rs. 3,156       (E) None of these
Three consecutive odd numbers are x, (x+2) and (x+4), or (x-2), x and (x+2), where x is an odd number.
Similarly, three consecutive even numbers are x, (x+2) and (x+4) or (x-2), x and (x+2) where x is an even number
If a number 'a' is multiplied by itself for n times, the product is called n th power of
'a'. This is written as an.
In an, a is called base and n is called index or exponent or power.

Laws of Indices

All simplification questions have to be solved based on BODMAS rule only.
B - Bracket
O - Of
D - Division
M - Multiplication
S - Subtraction
e.g. 1: What is 394 times 113? (SBI 2008)
(A) 44402             (B) 44632              (C) 44802           (D) 44522         (E) None of these
Sol:   394 × 113 = 44522,     hence answer (D)

2. What approximate value should come in place of the question mark (?) in the following question?  4780 ÷ 296 × (23)2 = ?
(A) 9870                (B) 6760                  (C)7590              (D) 3430           (E) 8540
Sol: 4780/296 × 529 = 8542.63

3. When 40% of first number is added to the second number the second number becomes 1.2 times of itself. What is the ratio between the first and second numbers?
(A) 2:3                  (B) 4:3                     (C) 1:2                  (D) 5:7                 (E) None of these
Sol: Let the first and second number be x and y

Posted Date : 25-07-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.